Covariant Wigner function approach to the Boltzmann equation for mixing fermions in curved space-time

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2 Citations (Scopus)

Abstract

Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved space-time. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to ℏ reproduces the previous result which was derived in the relativistic limit on the Minkowski background space-time. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obtained by solving the Boltzmann equation. Higher order effects of the ℏ-expansion are also briefly discussed.

Original languageEnglish
Pages (from-to)4469-4484
Number of pages16
JournalInternational Journal of Modern Physics A
Volume18
Issue number24
DOIs
Publication statusPublished - Sep 30 2003
Externally publishedYes

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fermions
gravitational effects
oscillations
expansion
neutrinos
vacuum

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

Cite this

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abstract = "Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved space-time. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to ℏ reproduces the previous result which was derived in the relativistic limit on the Minkowski background space-time. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obtained by solving the Boltzmann equation. Higher order effects of the ℏ-expansion are also briefly discussed.",
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AB - Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved space-time. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to ℏ reproduces the previous result which was derived in the relativistic limit on the Minkowski background space-time. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obtained by solving the Boltzmann equation. Higher order effects of the ℏ-expansion are also briefly discussed.

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